library(rstan)
library(survival)
library(tidyverse)
library(tidybayes)
library(scales)
library(survminer)
# data, parameters, model and generated quantities blocks
Stan_exponential_survival_model <- "
data{
int <lower=1> N_uncensored;
int <lower=1> N_censored;
int <lower=0> numCovariates;
matrix[N_censored, numCovariates] X_censored;
matrix[N_uncensored, numCovariates] X_uncensored;
vector <lower=0>[N_censored] times_censored;
vector <lower=0>[N_uncensored] times_uncensored;
}
parameters{
vector[numCovariates] beta; //regression coefficients
real alpha; //intercept
}
model{
beta ~ normal(0,10); //prior on regression coefficients
alpha ~ normal(0,10); //prior on intercept
target += exponential_lpdf(times_uncensored | exp(alpha+X_uncensored * beta)); //log-likelihood part for uncensored times
target += exponential_lccdf(times_censored | exp(alpha+X_censored * beta)); //log-likelihood for censored times
}
generated quantities{
vector[N_uncensored] times_uncensored_sampled; //prediction of death
for(i in 1:N_uncensored) {
times_uncensored_sampled[i] = exponential_rng(exp(alpha+X_uncensored[i,]* beta));
}
}
"
# prepare the data
set.seed(42);
require (tidyverse);
data <- read_csv('../data/necessary_fields.csv')
Rows: 2066 Columns: 7
── Column specification ───────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────
Delimiter: ","
chr (1): host_type
dbl (1): duration_months
lgl (5): major_releases, censored, high_rev_freq, multi_repo, high_author_count
ℹ Use `spec()` to retrieve the full column specification for this data.
ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.
N <- nrow (data);
data$high_author_count <- car::recode(data$high_author_count, "'TRUE' = 0; 'FALSE' = 1")
data$censored <- car::recode(data$censored, "'TRUE' = 0; 'FALSE' = 1")
X <- as.matrix(pull(data, high_author_count));
is_censored <- pull(data, censored)==0;
times <- pull(data, duration_months);
msk_censored <- is_censored == 1;
N_censored <- sum(msk_censored);
# put data into a list for Stan
Stan_data <- list (N_uncensored = N - N_censored,
N_censored = N_censored,
numCovariates = ncol(X),
X_censored = as.matrix(X[msk_censored,]),
X_uncensored = as.matrix(X[!msk_censored ,]),
times_censored = times[msk_censored],
times_uncensored = times[!msk_censored])
# fit Stan model
require(rstan)
exp_surv_model_fit <- suppressMessages(stan(model_code = Stan_exponential_survival_model, data = Stan_data))
sh: Data/bayesian: No such file or directory
sh: clang++ -mmacosx-version-min=10.13: command not found
Warning in system2(CXX, args = ARGS) : error in running command
Warning in file.remove(c(unprocessed, processed)) :
cannot remove file '/var/folders/q8/7tchbyvd1dj3hkgw5ffkk6ph0000gp/T//RtmpKsHNQc/file9c704d83fb54.stan', reason 'No such file or directory'
SAMPLING FOR MODEL 'bf5dbbde6a245330de71a285e3fe7c42' NOW (CHAIN 1).
Chain 1:
Chain 1: Gradient evaluation took 0.001053 seconds
Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 10.53 seconds.
Chain 1: Adjust your expectations accordingly!
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SAMPLING FOR MODEL 'bf5dbbde6a245330de71a285e3fe7c42' NOW (CHAIN 2).
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SAMPLING FOR MODEL 'bf5dbbde6a245330de71a285e3fe7c42' NOW (CHAIN 3).
Chain 3:
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SAMPLING FOR MODEL 'bf5dbbde6a245330de71a285e3fe7c42' NOW (CHAIN 4).
Chain 4:
Chain 4: Gradient evaluation took 0.000239 seconds
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# print model fit
print(get_seed(exp_surv_model_fit))
[1] 1781592037
# print fit summary
fit_summary <- summary(exp_surv_model_fit)
print(fit_summary$summary)
mean se_mean sd 2.5% 25% 50% 75% 97.5% n_eff Rhat
beta[1] 0.9610668 0.003469243 0.09864530 0.7662478 0.8964092 0.9599723 1.025412 1.157458 808.5063 1.0030074
alpha -5.5702904 0.003259977 0.09268295 -5.7530200 -5.6312316 -5.5684936 -5.507378 -5.387270 808.2966 1.0028752
times_uncensored_sampled[1] 101.4007616 1.579621665 99.28152824 3.1663896 30.0705682 71.1079952 141.571492 367.335410 3950.3061 0.9992525
times_uncensored_sampled[2] 99.8674940 1.650189014 98.81590701 2.6235553 29.0850175 69.0509403 142.613116 355.883333 3585.8023 0.9999019
times_uncensored_sampled[3] 99.7254321 1.606082397 100.17309805 2.8178707 29.3295996 69.2424462 138.136578 375.291482 3890.1520 1.0005881
times_uncensored_sampled[4] 101.5660981 1.611727202 98.53597710 2.6310402 30.8346605 72.8571719 140.246676 360.458331 3737.7184 1.0007518
times_uncensored_sampled[5] 98.6962559 1.690417174 100.59410450 1.9990443 26.8521824 66.1102421 135.098469 365.143576 3541.2555 1.0000183
times_uncensored_sampled[6] 101.4598013 1.620750674 100.03240473 2.5743604 29.7873639 71.6273625 138.879095 370.618112 3809.3335 0.9999513
times_uncensored_sampled[7] 101.1431563 1.634950386 104.09738844 2.3081476 29.1865746 70.2003937 137.658540 381.073256 4053.8765 0.9999765
times_uncensored_sampled[8] 98.9337840 1.583065017 99.35095712 2.5270233 29.3593913 68.6434380 138.402479 368.169193 3938.6429 0.9995024
times_uncensored_sampled[9] 101.6496298 1.565374770 98.06324682 2.5913941 30.2829320 73.7378852 140.908332 373.085534 3924.4236 0.9994005
times_uncensored_sampled[10] 102.4643298 1.661085391 103.96221644 2.6974187 29.1259119 69.8830345 142.351890 378.348536 3917.1224 1.0007666
times_uncensored_sampled[11] 99.8983379 1.564914995 102.75569355 2.7272146 28.1834477 68.2245622 135.800533 383.388905 4311.5188 1.0004416
times_uncensored_sampled[12] 103.8273646 1.668850449 104.10405948 2.4479161 28.4554992 70.7262366 145.691189 382.322586 3891.3518 0.9999383
times_uncensored_sampled[13] 100.9167185 1.602960451 105.23319844 2.6251072 28.6545466 66.9158948 135.110649 380.164265 4309.8279 1.0000070
times_uncensored_sampled[14] 100.3434487 1.691310420 101.51880870 2.4835215 27.2307201 68.3313511 140.962114 380.146838 3602.8516 1.0011187
times_uncensored_sampled[15] 99.9792842 1.677036474 104.09197843 2.4569254 29.5752085 67.3836452 135.115862 370.107965 3852.5609 0.9996538
times_uncensored_sampled[16] 98.9432885 1.538469434 96.50244932 2.7328610 30.0626784 69.7344608 137.253657 356.102743 3934.5850 1.0006864
times_uncensored_sampled[17] 100.5680984 1.593588526 101.07109474 2.3656542 29.0821363 70.2374611 140.553065 378.920948 4022.5509 1.0004719
times_uncensored_sampled[18] 98.1952798 1.540909553 96.64714695 2.3368066 29.0490755 68.2979261 139.083927 356.590003 3933.9042 0.9998619
times_uncensored_sampled[19] 99.4638958 1.501457159 96.41548754 2.3420991 29.7652979 70.2084221 139.412060 353.211124 4123.5163 1.0000883
times_uncensored_sampled[20] 100.1389257 1.551265855 100.39686227 2.7963286 29.3255387 67.7669214 136.378719 373.375593 4188.5896 1.0003627
times_uncensored_sampled[21] 101.3416623 1.596288946 102.31952362 2.5086553 28.3483812 68.8377345 141.559967 384.395139 4108.6014 0.9999264
times_uncensored_sampled[22] 103.0978279 1.632757628 102.93945763 3.0625646 29.9585805 71.2550232 141.784395 374.699024 3974.8460 0.9997074
times_uncensored_sampled[23] 100.8922851 1.547649201 98.33391699 2.9453731 28.8955884 72.0470565 141.863026 372.726888 4037.0267 1.0001818
times_uncensored_sampled[24] 103.7992741 1.905380858 101.49756641 2.9858914 29.6986331 71.3053140 143.610993 376.930974 2837.5771 1.0017859
times_uncensored_sampled[25] 99.3020157 1.620669233 100.96920723 3.0826676 29.2715722 68.1121017 137.548704 370.765488 3881.4064 1.0003501
times_uncensored_sampled[26] 102.4638590 1.734846786 104.37873161 2.6898286 28.6144758 69.8170094 138.826640 376.618414 3619.9434 0.9998252
times_uncensored_sampled[27] 102.6901808 1.643278270 102.18899071 2.5205700 31.2300601 72.8582956 138.536532 368.584367 3867.1053 1.0000300
times_uncensored_sampled[28] 99.1673112 1.533795120 97.46302386 2.3270354 28.3309493 69.5676199 137.330148 355.321715 4037.8024 1.0001796
times_uncensored_sampled[29] 98.9146521 1.641131260 98.69487651 2.6817901 28.6743417 67.9892968 139.392290 359.377369 3616.6175 1.0004195
times_uncensored_sampled[30] 99.7620452 1.534652680 98.93953682 2.7977234 28.8503989 69.6760369 138.129868 359.539162 4156.4211 1.0002208
times_uncensored_sampled[31] 102.4552118 1.705786729 101.28420729 2.3299213 30.4646982 70.2029180 140.733408 375.809153 3525.6078 0.9997550
times_uncensored_sampled[32] 104.0016602 1.627267226 103.79922279 2.7568610 30.2577453 72.4506572 143.103245 385.081924 4068.8385 0.9995274
times_uncensored_sampled[33] 102.1136935 1.620753462 100.64987336 2.6288861 29.2045194 71.8093887 140.752185 370.924405 3856.4930 1.0002365
times_uncensored_sampled[34] 101.4097733 1.653739910 102.44295821 2.3306596 28.1569750 70.9830403 141.452379 385.943776 3837.3358 0.9999280
times_uncensored_sampled[35] 99.4260666 1.573452004 98.82834651 2.5782976 29.7909258 70.6565222 139.491705 371.499811 3945.0822 1.0010901
times_uncensored_sampled[36] 98.6213940 1.642587741 100.32401365 2.0679316 26.5304457 69.1079149 137.000961 364.615390 3730.3763 1.0002556
times_uncensored_sampled[37] 99.6320020 1.532822403 96.79202022 3.1174462 29.4904568 71.3058339 137.114916 361.657812 3987.4517 0.9998778
times_uncensored_sampled[38] 100.6688368 1.580810575 99.35169261 2.6760522 28.8581944 69.4260044 141.599705 369.192804 3949.9434 0.9995329
times_uncensored_sampled[39] 99.8605247 1.606684079 99.66322137 2.3737557 29.5792362 69.6953472 139.126799 365.722000 3847.7678 1.0005542
times_uncensored_sampled[40] 100.6406664 1.644937771 99.60585349 2.4320771 28.6913451 70.4824327 141.818871 359.913034 3666.6611 0.9993083
times_uncensored_sampled[41] 103.8623635 1.634267871 102.06391247 2.4844398 29.7329374 73.0194921 144.543404 374.970685 3900.2993 1.0006517
times_uncensored_sampled[42] 101.7245265 1.576633585 99.96115449 2.1828391 29.1317177 71.3159636 141.323483 367.665765 4019.7679 1.0005205
times_uncensored_sampled[43] 103.9100094 1.647498906 103.29140218 2.9860819 32.0317672 73.8496706 141.840128 380.805314 3930.7740 0.9991513
times_uncensored_sampled[44] 100.6544524 1.592531682 99.54032536 2.8053084 30.1159524 70.6961084 138.980894 368.464521 3906.8069 1.0003501
times_uncensored_sampled[45] 99.8773502 1.608043418 99.93374210 2.6648112 28.9467675 68.3868849 139.002255 369.260868 3862.1466 1.0001708
times_uncensored_sampled[46] 98.7347071 1.617593512 100.77150371 2.5432323 28.4647770 67.4847609 136.639953 372.219783 3880.9378 0.9997949
times_uncensored_sampled[47] 98.6015038 1.617431472 100.98683748 2.4497314 27.9814346 68.2326300 134.235876 376.521962 3898.3225 0.9996416
times_uncensored_sampled[48] 101.3695341 1.596158544 103.31799526 2.7444437 27.9951623 69.3620589 142.438706 382.107312 4189.8636 0.9995612
times_uncensored_sampled[49] 98.9684035 1.603559749 100.01520097 2.4068339 28.5877136 70.9291945 136.476897 374.513017 3890.1086 0.9991667
times_uncensored_sampled[50] 100.0600020 1.654733731 103.18179697 2.5274968 27.9708746 67.8523456 137.749604 380.082290 3888.2120 0.9998109
times_uncensored_sampled[51] 100.6339179 1.668504757 100.90474014 2.6580141 28.0223386 69.8169823 138.893476 377.272925 3657.3644 0.9994740
times_uncensored_sampled[52] 101.2733583 1.618181032 100.35192055 2.4305453 30.2455717 71.3383310 140.625370 364.934841 3845.8927 0.9991729
times_uncensored_sampled[53] 99.6968587 1.592663669 100.43574127 2.1989698 29.1312226 69.5604673 136.320885 373.313665 3976.7513 0.9995807
times_uncensored_sampled[54] 99.2555014 1.685804779 97.71950624 2.3769064 29.4269087 70.3015035 135.705418 357.786640 3360.0672 1.0003406
times_uncensored_sampled[55] 100.7606272 1.602585914 103.20357411 2.5615390 29.1158433 68.0186372 136.830168 383.056190 4147.1222 0.9994995
times_uncensored_sampled[56] 98.8235280 1.558602397 98.26204237 2.1952417 26.4684516 67.7546516 141.245509 357.120265 3974.6683 0.9996522
times_uncensored_sampled[57] 101.1561216 1.664334764 103.87590151 2.5605195 28.9415522 69.4458671 137.609171 378.696127 3895.3658 1.0001552
times_uncensored_sampled[58] 100.0354126 1.619929128 99.84477294 2.3379141 29.6062871 68.8314915 137.488470 363.528799 3798.9068 0.9999869
times_uncensored_sampled[59] 100.6814514 1.586591788 100.76473871 2.5277112 30.0326446 69.4509516 137.655035 378.190391 4033.5437 0.9998752
times_uncensored_sampled[60] 100.4849704 1.545261806 100.14102192 2.4856512 28.9254610 69.6004950 142.697606 366.139571 4199.7158 0.9997204
times_uncensored_sampled[61] 100.3823089 1.590368193 101.62470852 2.2960232 29.1733661 69.6809506 137.180454 371.023317 4083.2245 1.0006545
times_uncensored_sampled[62] 102.1880806 1.593646404 100.92367347 3.2054312 31.8402350 71.8708046 139.934912 374.436975 4010.5337 0.9997584
times_uncensored_sampled[63] 102.1109559 1.678009997 102.63049620 2.2101561 28.5714370 70.9498818 141.385892 371.793190 3740.7938 0.9998071
times_uncensored_sampled[64] 101.2824505 1.632432351 98.64354758 2.6577523 30.3843893 70.1015489 143.497273 365.911625 3651.4636 1.0002328
times_uncensored_sampled[65] 100.5779011 1.607443956 100.88651908 2.4901288 28.3332767 69.8325328 140.735568 367.641086 3939.0781 0.9995665
times_uncensored_sampled[66] 99.8520256 1.530828631 98.91160690 3.1543502 28.9649613 70.2495458 138.739215 368.100469 4174.8547 0.9994002
times_uncensored_sampled[67] 100.6833393 1.565037048 98.57380346 2.2888389 29.5237410 68.8641914 141.684028 367.858006 3967.1058 1.0006201
times_uncensored_sampled[68] 102.3528226 1.639415797 102.79093217 2.7641136 29.5535080 70.4509394 141.690821 368.664738 3931.2565 0.9993744
times_uncensored_sampled[69] 101.1736573 1.589817746 103.10678575 2.4018895 27.6702823 70.3216005 140.342264 381.419243 4206.1022 1.0000502
times_uncensored_sampled[70] 100.6658694 1.588249256 98.77472249 2.3565076 28.6109942 69.7953940 144.573921 357.619236 3867.7137 0.9994157
times_uncensored_sampled[71] 99.8934172 1.509919733 96.30698908 3.0097468 30.0606571 70.2152167 140.633948 357.327229 4068.2524 0.9996342
times_uncensored_sampled[72] 97.7411180 1.603410819 99.70578290 2.7640139 28.2390705 67.4748281 134.805557 373.671190 3866.7944 0.9999274
times_uncensored_sampled[73] 99.9086500 1.658712014 98.72480948 2.3969666 28.7753713 69.3831869 139.772320 364.940669 3542.5063 0.9994832
times_uncensored_sampled[74] 102.2037839 1.618139570 103.29394196 2.3335256 28.3188644 70.0509134 142.412347 384.518996 4074.9074 1.0002697
times_uncensored_sampled[75] 101.3108096 1.685144920 101.99806401 2.4177107 28.6058668 67.3665735 141.808731 381.514382 3663.6109 0.9998487
times_uncensored_sampled[76] 100.0380304 1.631054136 102.96088829 2.2003227 27.0576554 68.1600702 138.675137 384.352661 3984.8118 0.9996969
times_uncensored_sampled[77] 101.6743376 1.597353138 100.58480463 2.6376923 30.1471815 70.3125716 140.368644 371.158289 3965.1797 1.0001037
times_uncensored_sampled[78] 98.2503343 1.634409147 100.17178302 2.0639269 28.9163959 66.9410465 137.019832 363.234240 3756.3776 0.9998128
times_uncensored_sampled[79] 100.5972538 1.642183993 100.03140564 2.6701801 29.5732454 70.1697681 140.106848 363.991113 3710.4716 0.9996782
times_uncensored_sampled[80] 102.6351587 1.638485616 104.04326114 2.7876907 29.5408746 70.6619431 140.861902 386.779929 4032.2054 0.9992672
times_uncensored_sampled[81] 100.2649587 1.652985511 102.70449978 2.7923013 28.8636105 68.1022840 136.479248 375.838879 3860.4759 0.9993682
times_uncensored_sampled[82] 100.0768307 1.567083951 100.01916616 2.3937711 28.4415317 68.3720457 139.903532 375.719381 4073.6333 0.9999585
times_uncensored_sampled[83] 100.1468588 1.531410132 97.59235073 2.3141427 28.9037724 71.1687203 139.923489 347.936984 4061.1453 0.9997024
times_uncensored_sampled[84] 103.9296480 1.673775959 105.28222510 2.4244231 29.5937324 71.0708172 143.306291 388.598090 3956.5391 0.9994414
times_uncensored_sampled[85] 102.1305428 1.655146536 103.71796944 2.2370995 29.2913203 69.2358323 140.994049 381.185355 3926.7668 1.0000299
times_uncensored_sampled[86] 98.9726324 1.571608482 99.97827138 2.6617436 28.2947595 68.7545149 137.059297 362.258778 4046.9004 0.9992148
times_uncensored_sampled[87] 98.6867424 1.663617083 100.39366596 2.5429066 27.8162488 66.4037481 135.035546 366.279187 3641.7144 1.0005194
times_uncensored_sampled[88] 102.0335427 1.554155985 100.34463410 2.6562723 28.6932637 71.9099501 142.871107 374.665348 4168.6852 0.9997515
times_uncensored_sampled[89] 98.9898092 1.595903899 101.77530496 2.5908472 27.4182303 67.7155495 136.105703 371.040805 4066.9736 1.0004778
times_uncensored_sampled[90] 101.5090084 1.636672841 103.59211906 2.5084052 27.4999140 68.3907634 140.077744 368.646561 4006.1728 0.9996835
times_uncensored_sampled[91] 98.1556334 1.576525273 97.04898713 2.3652807 27.5780474 68.0264928 137.679495 355.848367 3789.4845 1.0007971
times_uncensored_sampled[92] 99.5970802 1.666685203 100.82706148 2.2698478 27.9087690 67.9152724 138.060001 365.286256 3659.7133 0.9994646
times_uncensored_sampled[93] 101.5815642 1.655934829 101.61201619 2.0763661 28.0261219 70.2450552 140.059959 373.962017 3765.3353 1.0000585
times_uncensored_sampled[94] 99.7524186 1.557855972 98.03061430 2.5600517 28.3042517 69.8383784 139.381542 353.097261 3959.7598 0.9997430
times_uncensored_sampled[95] 100.7637657 1.606235268 100.33513152 2.4639736 29.0499588 70.4971321 142.230029 364.628866 3902.0042 0.9998357
times_uncensored_sampled[96] 101.5112267 1.689558031 104.14613749 2.0722841 28.7269151 70.2354480 139.521292 377.751501 3799.6195 0.9995552
times_uncensored_sampled[97] 101.9205645 1.675397947 101.53484738 2.5774725 28.7931825 70.1994251 144.568393 366.343129 3672.7747 1.0004150
times_uncensored_sampled[98] 103.9088797 1.718623618 105.83285306 2.6449154 28.1632443 70.8990062 146.221107 391.305317 3792.0972 1.0004793
[ reached getOption("max.print") -- omitted 678 rows ]
exp_surv_model_draws <- tidybayes::tidy_draws(exp_surv_model_fit)
exp_surv_model_draws